Permutation of natural numbers induced by the automorphism gt-df->bf (switch from the Depth First to the Breadth First coding for the general trees/parenthesizations) acting on the parenthesizations encoded by A014486.

When restricted to the subset of plane binary trees, produces the automorphism A057118 and being "self-embeddable", this allows us also to construct the permutation A072620 (A072622). [See comment at A072088].